Problem: Simplify the following expression: $\sqrt{18}-\sqrt{32}+\sqrt{50}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{18}-\sqrt{32}+\sqrt{50}$ $= \sqrt{9 \cdot 2}-\sqrt{16 \cdot 2}+\sqrt{25 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{2}-\sqrt{16} \cdot \sqrt{2}+\sqrt{25} \cdot \sqrt{2}$ $= 3\sqrt{2}-4\sqrt{2}+5\sqrt{2}$ Finally, simplify by combining the terms. $= ( 3 - 4 + 5 )\sqrt{2} = 4\sqrt{2}$